# Is sea level rise accelerating?

## What the science says...

Looking at global data (rather than tide gauge records just from the U.S.) show that sea level rise has been increasing since 1880. The recent rate of sea level rise is greater than its average value since 1930. As for future sea level rise, these predictions are based on physics, not statistics.

## Climate Myth...

Sea level rise is decelerating

"A former research director with the Army Corps of Engineers and a former civil-engineering professor at the University of Florida decided to put the sea-rise claims to the test. They gathered U.S. tide-gauge readings from 57 stations where water levels had been continuously recorded for as long as 156 years. The result did suggest the sea level was increasing in the western Pacific, but this was offset by a drop in the level near the Alaskan coast. “Our analyses do not indicate acceleration in sea level in U.S. tide gauge records during the 20th century,” the study’s authors concluded. “Instead, for each time period we consider, the records show small decelerations that are consistent with a number of earlier studies of worldwide-gauge records." (Washington Times)

A paper by Houston & Dean studies 57 tide gauge records from the U.S. (including Hawaii and oceanic territories) and concludes that sea level rise has not *accelerated*. In fact the authors seem to go out of their way to state that the average result shows *deceleration* at every opportunity. But there are some big questions about their analysis. Why do they use tide gauge records from just U.S. stations? Why not a global sample? Why use individual tide gauge records when we have perfectly good combinations, from much larger samples, which give a global picture of sea level change and show vastly less noise? Why do they restrict their analysis to either the time span of the individual tide gauge records, or to the period from 1930 to 2009? Why do they repeatedly drone on about “*deceleration*” when the average of the acceleration rates they measure, even for their extremely limited and restricted sample, isn’t statistically significant?

But the biggest question of all is: what’s the big deal?

Here’s some sea level data, in fact two data sets. One is a global combination of tide gauge records by Domingues et al. (2008). Using around 500 tide gauge records globally, it’s the latest version of the “Church & White” dataset. The other is satellite data:

I averaged the two data sources during their period of overlap, and computed a smoothed version:

This is a *global* data set, and it’s a worldwide average so its shows vastly less noise than individual tide gauge records. We could even use it to look for acceleration or deceleration in sea level rise. But one thing we should **not** do is restrict consideration to the quadratic term of a quadratic polynomial fit from 1930 onward. That would be pretty ignorant — maybe even misleading.

As so often happens, one thing to be cautious of is that the noise shows autocorrelation. As Houston & Dean point out, the Church & White data since 1930 are *approximately* linear, so to get a conservative estimate of the autocorrelation I used the residuals from a linear fit to just the post-1930 data and fit an ARMA(1,1) model.

If we compute the linear trend rate for all possible starting years from 1880 to 1990, up to the present, we get this:

According to this, the recent rate of sea level rise *is* greater than its average value since 1930. Significantly so (in the statistical sense), even using a conservative estimate of autocorrelation. But the increase itself hasn’t been steady, so the sea level curve hasn’t followed a parabola, most of the increase has been since about 1980. How could Houston & Dean have missed this?

Here’s how: first, they determined the presence or absence of acceleration or deceleration based only on the quadratic term of a quadratic fit. That utterly misses the point. Changes in the rate of sea level rise don’t have to follow a parabola, since 1930 or any time point you care to name. In fact, by all observations and predictions, they have not done so and will not do so.

Second, by using individual tide gauge records, the *noise* level is so high that you can’t really hope to find acceleration or deceleration of any kind, with any consistency. Not using quadratic fits, and certainly the non-parabolic trend which is present can’t be found in such noisy data sets.

Even so, we can also fit a quadratic (as Houston & Dean did), and estimate the *acceleration* (which is twice the quadratic coefficient):

Well well … it looks like starting at 1930 is the way to get the *minimum* “acceleration” by this analysis method. Could that be why Houston & Dean chose 1930 as their starting point?

If we restrict to only the data since 1930, as Houston & Dean did, and fit a quadratic trend, we get this:

Can you tell, just by looking, whether it curves upward or downward? Clearly, the parabolic fit doesn’t show much acceleration or deceleration, if any. We can get a better *picture* by first subtracting a linear fit, then fitting a parabola to the residuals?

That answers the question: the quadratic fit shows acceleration in the Church & White data. But, when autocorrelation is taken into account, the “acceleration” is **not** statistically signficant.

But — just because the data don’t follow a parabola, doesn’t mean that sea level hasn’t accelerated. Let’s take those residuals from a linear model, and fit a *cubic* polynomial instead:

Well well … there seems to be change after all, with both acceleration and deceleration but most recently, acceleration. And by the way, this fit *is* significant.

And now to the really important part, which is not the math but the physics. Whether sea level showed 20th-century acceleration or not, it’s the century coming up which is of concern. And during this century, we expect acceleration of sea level rise because of *physics*. Not only will there likely be nonlinear response to thermal expansion of the oceans, when the ice sheets become major contributors to sea level rise, they will dominate the equation. Their impact could be tremendous, it could be sudden, and it could be horrible.

The relatively modest acceleration in sea level so far is *not* a cause for great concern, but neither is it cause for *comfort*. The fact is that statistics simply doesn’t enable us to foresee the future beyond a very brief window of time. Even given the observed acceleration, the forecasts we should attend to are not from statistics but from physics.

Many thanks to Tamino from Open Mind for allowing us to republish his post So What?

Advanced rebuttal written by Tamino

**Update July 2015**:

Here is a related lecture-video from Denial101x - Making Sense of Climate Science Denial

This rebuttal was updated by Judith Matz on September 13, 2021 to replace broken links. The updates are a result of our call for help published in May 2021.

Last updated on 8 July 2015 by pattimer. View Archives

Steve Caseat 00:07 AM on 28 August, 2011Here’s some sea level data , in fact two data sets. One is a global combination of tide gauge records by Domingues et al. (2008, Nature, 453, 1090-1094, doi:10.1038/nature07080). Using around 500 tide gauge records globally, it’s the latest version of the “Church & White” dataset. The other is satellite data: ... If we compute the linear trend rate for all possible starting years from 1880 to 1990, up to the present, we get this:The above chart, as I understand it, uses data from 1880 all the way up to the present, but the plot only covers 1880 to 1990. The last 20 years have been left off. If the plot were to continue right up to the present the time line would become very erratic as the sample size approaches unity and becomes meaningless. Essentially large sample sizes early in the time line are compared with numerically smaller samples of more recent data. In everyday language, it's comparing apples and oranges. The cutoff at 1990 would indicate that a 20 sample size is appropriate. So why not look at 20 year slices of trend rate back through time and see how they compare? And lets use all of the data all the way to the present. So if we compute the linear trend rate for all possible 20 year periods starting with 1807 - 1827 then 1808 - 1828 and so on up to the present, we get this: An entirely different picture is painted when each data point represents an equal sample size. The early years are erratic because of a small number of tide gage records. The above link "some sea level data" didn't work for me, I used data from the PSMSL that dates from 1807 from over 1200 tide gages. The data is grouped and averaged by coastlines and the median value take for each year in the time line. I assume that the Church & White/satellite data would plot out in a similar fashion as above.Response:[DB] From Church & White 2011:

And using 16-years trends:

[Source]

Tom Curtisat 02:20 AM on 28 August, 2011Steve Caseat 05:13 AM on 28 August, 2011muoncounterat 06:15 AM on 28 August, 2011the forecasts we should attend to are not from statistics but from physics.Bob Lacatenaat 07:17 AM on 28 August, 2011Tom Curtisat 10:18 AM on 28 August, 2011I am disputing your use of a data set which is never geographically representative, and which changes the representation of various regions over timein order to determine those trends. As ever, DB provides the best information, and you would do well to look carefully at the second figure (fig 8) in his inline comment. Applying 16 year trends on a consistent and representative data set shows a very distinct pattern to that shown from your simple mean of the PSMSL data set.Steve Caseat 18:45 PM on 28 August, 2011Tom Curtisat 19:55 PM on 28 August, 2011notwhat Tamino has done. Tamino is testing a particular claim, ie, that the rate of change in global sea level hasdeceleratedover the course of the twentieth century (or at least since 1930). Plotting the trend to end point for each year in succession will, as you suggest, exagerate the magnitude of more recent trends relative to older trends. It will show greater variability in the more recent trend. But it will not determine whether the recent trends are larger than the long term trend, or smaller. If in fact the rate of change of sea level was decelerating as is claimed by Houston and Dean, then the most recent trends would be smaller than the long term trends, and plotting a graph such as Tamino's third figure will show a steady line falling away towards zero at the end. So if that is your point, you have no point. You would do well to reread Tamino's post and pay attention to the other more important statistical techniques Tamino applies to determine the evolution of the rate of change of sea level over the 20th century. 2) If you want to introduce your chart as evidence, you need to defend its construction. If you don't want to defend its construction, you ought to withdraw it. As it stands, however, it appears you want to make use of a graph in which artifacts of the data will introduce a very large amount of noise. If you are simply trying to make a logical point about Tamino's analysis, I do not understand why you insist on the accuracy of your graph when you could make the same points using the graph provided by DB inline @1. You, however, insist on sticking with your graph, which makes me suspect some feature of that graph is important to the point you are trying to make. But to the extent that your graph differs from that supplied by DB, there is very good reason to think that the difference is due to noise introduced by your methods.Steve Caseat 22:22 PM on 28 August, 2011not, the title of this discussion is:Is sea level rise accelerating?If you go to the CU Sea Level Research Group you will find this chart: and a link to the data: Raw data (ASCII) If you plot that data out in Excel with 60 day smoothing just like Colorado Research Group's chart and add a second order polynomial Trend Line instead of a linear trend, it will look like this: I would say that according to that sea level isnotaccelerating.Response:[mc] Reset image width to 450muoncounterat 22:47 PM on 28 August, 2011Sea level was stable from at least BC 100 until AD 950. Sea level then increased for 400 y at a rate of 0.6 mm/y, followed by a further period of stable, or slightly falling, sea level that persisted until the late 19th century. Since then, sea level has risen at an average rate of 2.1 mm/y, representing the steepest century-scale increase of the past two millennia.I'd suggest, as others threads already have, that long-term pattern is described accurately as 'accelerating.' And that does not even reflect the 3.2 mm/yr from the graph you posted above.Tom Curtisat 23:06 PM on 28 August, 2011Steve Caseat 23:47 PM on 28 August, 2011Response:[DB] In your desire to prosecute your agenda, you continue to cherry-pick by only using a small portion of the data available.

That is muoncounter & Tom Curtis' point, and the entire point of this post you are commenting on.

If you want to be taken seriously, you will have to rectify that & address the totality of the data, as Tamino did.

Steve Caseat 00:03 AM on 29 August, 2011Tom Curtisat 00:20 AM on 29 August, 2011Steve Caseat 03:10 AM on 31 August, 2011Response:[DB] Speculations into motive snipped. Either formulate a comment that doesn't cast aspersions into other's integrity or don't post here.

Future comments containing such speculations and aspersion will be deleted outright.

Eric the Redat 08:36 AM on 31 August, 2011Response:[DB] In your ongoing desire to prosecute your agenda, you continue to cherry-pick by focusing on a small, statistically insignificant, portion of the data available.

skywatcherat 10:39 AM on 31 August, 2011Steve Caseat 20:42 PM on 31 August, 2011Station ID 1234 Station Name SIROS Data available 1969 - 2009 Data used 1974.042 - 2009.958 Data not used 1969; 1971; 1972 Change in slope +1.8 mm/yr.

Maybe some one who has plunked down the cash for Church et al. (2004) can summarize what the editing criteria is.

Response:[DB] If you were perchance to take the attitude of genuinely trying to research this instead of ascribing untowards motives to those publishing research and if you perchance were to genuinely ask for help when stuck instead of just airing complaints about paywalls, then perhaps someone might help you.

Like pointing out that Church et al 2004 was available for free opus download from the publisher, Journal of Climate:

http://journals.ametsoc.org/doi/pdf/10.1175/1520-0442%282004%29017%3C2609%3AEOTRDO%3E2.0.CO%3B2

Or that the data for Church et al 2004 appears to be available for free opus download at:

ftp://ftp.marine.csiro.au/pub/white/recons_1950_2001_ib_gia_remseas.nc.gz

Briefly, this data set is

on a 1° × 1° × 1 month grid

I'm certain you have been doing the above per established standards in your analysis.

Total time to research this: 6 minutes

Total time to write this up: 7 minutes

Steve Caseat 21:59 PM on 31 August, 2011Steve Caseat 22:02 PM on 31 August, 2011Response:[DB] You're welcome; anytime.

Bob Lacatenaat 23:09 PM on 31 August, 2011Steve Caseat 00:38 AM on 1 September, 2011Response:[DB]

"The satellite record date happened to start in 1993. That's the way it is. That you want to complain about it is isn't anything I can do much about."You continue to cherry-pick by only using a small portion of the data available. Satellites only represent a portion of the data available to us. The consiliance of these datasets paints a different picture:

Your laser-focus on the most recent period of data while ignoring that which came before it blinds you to the larger trend while magnifying the natural variability inherent in the system.

In a nutshell, you can't see the forest because you have a tree in the way. That's the way it is.

Rob Paintingat 01:22 AM on 1 September, 2011Bob Lacatenaat 01:51 AM on 1 September, 2011Steve Caseat 04:14 AM on 1 September, 2011Record..Status..........Reason 1159....RLR 1950....Met -256....eliminated......Records >2 years -1063...eliminated......Redundant -95.....eliminated......beyond TOPEX/Poseidon range -37.....eliminated......<250 km to Alt grid point. 1658....records for further assessment. ??......eliminated......Disagreement nearby records ??......eliminated......Locations ??......eliminated......Fragmented ??......eliminated......Noise ??......eliminated......Residual trends <10 mm/year -713....Eliminated......For above 5 reasons? (1658-945=713) 945.....combined -491....eliminated......by combination 454.....records for further assessment. -28.....eliminated......No useful data 426.....records for further assessment.Comments: Really, because Topex/Poseidon didn't cover the range they tossed the data? I don't think that makes sense, but I suppose there's a reason for that. In the text they go from 1658 records down to 945 records but don't give us any numbers as to how many were eliminated for the five reasons tabulated above. Residual Trends <10 mm/yr is reasonably objective. The other four listed are somewhat subjective without any guidelines as to what constitutes unsuitable locations, too much noise, too much fragmentation, or how much disagreement with other records is allowed or how near by they must be. After combining the 945 records there was another group of records eliminated for having no useful data. What was not useful? Perhaps in the data file that defies downloading for me, that is spelled out and each and every deletion is annotated as to how the criteria were met. As it stands right now and as far as I’m concerned, there is room for some subjectivity in perhaps several hundred deletions of data. A simple analysis of the data yields one thing, and the process along with the above editing criteria yields the opposite. Now even though there's a difference in sign, if the two time lines were close no one would care, but as you can see, they're not. The above is not the same as Reconstructed GMSL for 1880 to 2009 Which is linked at the top of this page but the treatment of the data is likely to be similar.Response:[DB] Fixed tags.

The most likely reason for your lines diverging is that you are doing something wrong. I suggest you contact Dr. Church or Dr. White (or Tamino, as this is his post) for advice.

That would be the skeptical thing to do.